You have been hired to provide statistical consulting for th

You have been hired to provide statistical consulting for the United States Navy. The Navy wishes to evaluate how many hours of labor per month are needed to meet its medical needs. Specifically, your responsibility is to help the Navy in describing the number of monthly labor hours used in a sample of naval hospitals. Additionally, your task will be to assess the relationship between the number of monthly labor hours used and other variables provided by a sample of twelve naval hospitals.

The data set containing the sample of twelve naval hospitals is given below. The last six hospitals in the sample are teaching/training hospitals and the first six hospitals are not. In addition to type of hospital, the other study variables include:

-- Hours (number of monthly labor hours used)

-- X-Rays (number of monthly X-ray exposures)

-- Bed-Days (number of monthly occupied bed days)

-- Length (average length of a patient’s stay in days)

Hospital

Hours

X-Rays

Bed-Days

Length

566

2463

473

4.5

696

2048

1339

6.9

1033

3940

620

4.3

1611

5723

1497

5.5

1613

11520

1365

4.6

3503

20106

1365

6.1

1603

6505

568

3.9

1854

5779

620

5.6

2160

5969

568

5.2

2305

8461

1497

6.2

3571

13313

1687

5.9

3741

10771

1639

4.9

Enter the data set containing the sample of 12 hospitals into an Excel spreadsheet.

add the Teaching/Training qualitative variable to your data set. Specifically, if a particular hospital is a teaching/training hospital, then the variable teaching/training should be set to 1 and if a hospital is not a teaching/training hospital, the variable teaching/training should be set to 0.

1. Summarize the number of monthly labor hours used in the sample of 12 hospitals using the appropriate descriptive statistics. Provide an interval estimate for the average number of monthly labor hours used for all naval hospitals. Use 95% level of confidence for the prediction. (1point)

2. As there is reason to believe that the number of monthly labor hours used may be at least partially explained by other variables, the Navy has suggested that the relationship between each of the other quantitative variables and number of monthly labor hours be assessed.

Graphically show the linear relationship between each of the other quantitative variables and the hours of labor used. Which of the other quantitative variables has the strongest linear relationship with hours of labor? Why?(1.5point)

3. You want to build a regression model to estimate the number of hours of labor used for a given month.

Estimate the regression equation using the number of hours of labor used and the quantitative variable you selected in question 5b.

Provide the least squares estimated regression equation and interpret the regression coefficients.( 2.5 points)

What percentage of the variation in the number of labor hours used has been explained by the estimated regression equation? Is this a useful amount? (0.5 point)

How many hours of labor would be expected to be used for a naval hospital that has characteristics identical to those of hospital #1? Calculate the value of the residual. (0.5 point)

4. The Navy believes that the number of labor hours used is influenced by all the other variables in the data set.

Estimate the multiple regression model for the data based on all of the variables including the teaching/training variable. Provide the equation. (0.5 point)

Set up and provide the hypotheses to test whether the multiple regression model as a whole is significant. At 0.05 level of significance what is your conclusion? (1 point)

Interpret the value of the regression coefficient for X-rays from the estimated multiple regression equation. (1point)

Test to determine if there is a linear relationship between X-Rays and the number of monthly labor hours used . At the 0.05 level of significance, what is your conclusion? (1point)

Use the estimated multiple regression equation to predict the number of monthly labor hours used for the first hospital in the sample. Calculate the value of the residual. (0.5 point)

The Navy believes that Teaching/Training hospitals will have lower amount of labor hours used after adjusting for each of the other independent variables. Do your results support this belief? Why or why not? (1 point)

Given the three estimation methods (univariate, bivariate, and multivariate) presented in this report for estimating labor hours which would you recommend be used? Why? (1 point)

Hospital	Hours	X-Rays	Bed-Days	Length
1	566	2463	473	4.5
2	696	2048	1339	6.9
3	1033	3940	620	4.3
4	1611	5723	1497	5.5
5	1613	11520	1365	4.6
6	3503	20106	1365	6.1
7	1603	6505	568	3.9
8	1854	5779	620	5.6
9	2160	5969	568	5.2
10	2305	8461	1497	6.2
11	3571	13313	1687	5.9
12	3741	10771	1639	4.9